In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous-time signals (often called “analog signals”) and discrete-time signals (often called “digital signals”). It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth.
The continuous analog data must be sampled at discrete intervals that must be carefully chosen to ensure an accurate representation of the original analog signal. It is clear that the more samples taken (faster sampling rate), the more accurate the digital representation, but if fewer samples are taken (lower sampling rates), a point is reached where critical information about the signal is actually lost.
The Nyquist Theorem, also known as the sampling theorem, is a principle that engineers follow in the digitization of analog signals. For analog-to-digital conversion to result in a faithful reproduction of the signal, according to the Nyquist Theorem, the sampling rate must be at least twice the highest analog frequency component as shown in FIG. 1.
There are times that the analog signal spectrum is slightly shifted from the zero Hz frequency as shown in FIG. 2. This type of signal is called low intermediate frequency (IF) signal. In this case there are two approaches. One is to shift the analog signal spectrum to zero Hz in analog domain and then similar to FIG. 1 use Nyquist sampling and digitize the analog signal. In the first approach there is need for analog circuitry for shifting the spectrum to zero Hz which results in cost and power consumption. In a second approach Nyquist theorem is used to digitized the low IF analog signal and then shift the spectrum in digital domain to zero Hz. This approach requires higher sampling rate, a higher rate analog-to-digital convertor and slightly signal processing in digital domain.
In another scenario the analog signal is centered at a high IF frequency as shown in FIG. 3. In this scenario there are three solutions. One similar to low IF down convert the analog signal to zero Hz frequency and then digitized. Again this approach results in cost and power consumption. The second approach is to sample the high IF analog signal which requires very high rate analog-to-digital convertor and considerable signal processing that results in cost and power consumption. The third approach is to use sub-harmonic sampling. In sub-harmonic sampling in order to be able to recover analog signal information in digital domain the sampling rate should be equal or higher than twice the bandwidth of the analog signal. The choice of the sampling rate needs to simplify the required signal processing in digital domain. FIG. 4 demonstrate how sub-harmonic sampling is used to digitize and subsequently shift the digital signal to zero Hz for a complex signal with real and imaginary components.
If the sampling rate is smaller than what was defined above, then a phenomenon called aliasing will occur in the analog signal bandwidth as shown in FIG. 5. It can be seen that aliasing affects the dynamic range of the signal since the upper part of the signal spectrum is affected. This condition will result in reduction in overall signal-to-noise at the higher frequencies, and could result in the distortion due to aliased out-of-band tones or harmonics as shown in FIG. 5.
It should be cleared by now, that for a given analog input bandwidth; the requirements for anti-aliasing filter are related not only to the sampling rate, fs, but also to the desired system dynamic range. For burst type analog signals that have harmonics spread over a very large bandwidth like the one shown in FIG. 6 defining the requirements of the anti-aliasing filter is even more difficult. One also has to consider the limitations of analog-to-digital quantization noise and other non-linearity.
This application discloses a novel non-uniform sampling technique for a burst type signal. The analog signal is digitized with high sampling rate to maintain harmonics at higher frequencies and consequently the integrity of the analog signal. Then by using non-uniform sampling technique the most significant samples are selected for further processing which results in overall cost and power consumption reduction.
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